Doesn’t the rule say that the weak forms of is and has may not occur in final position, rather than that ’s may not do so?
– Barrie EnglandDec 19 '13 at 17:53

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I seem to remember that let's is an example of grammaticalization, but I don't think that applies to he's, she's etc. Apart from anything else, the contracted part in let's is the all-important pronoun us (which has true meaning in context), whereas in the others it's just an almost superfluous is (simply a "helper verb" required by grammatical considerations).
– FumbleFingersDec 19 '13 at 18:28

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I think the correct formulation of the rule is: you can't contract is, are, has, had, or have at the end of of a sentence.
– Peter Shor Dec 19 '13 at 18:41

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@Peter,tchrist: It seems to me rule is more like you can't contract auxiliary verbs at the end of a sentence. But if indeed the permissible forms (as opposed to the unacceptable ones) can be fully defined by "rules", it's not obvious to me why we only accept My cellmate said, "Let's have a party tonight". But the prison guards wouldn't let us. Where expanding the first instance would be hopelessly archaic, and contracting the second would be a complete no-no.
– FumbleFingersDec 19 '13 at 20:51

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I think your interesting example shows that "let's" is not a contraction.
– Greg LeeMar 24 '16 at 16:16

are, I think, always interchangeable on grammatical grounds (though some older Church leaders might consider "Let's pray" over-informal, and often sentences like "Let us go to the cinema tonight" would sound far too stilted).

However, "let us . . ." meaning "allow us to" is never rendered "let's". Idioms often seem to have their own rules.